#
*INTRODUCTORY LECTURES *

ON RINGS AND MODULES

#
CLASS NOTES

by John A. Beachy
These online notes are intended to help students
who are working through the text.
The notes will include some historical comments and background material,
together with supplementary problems and solutions.

You will soon see that very little has been completed.
I had hoped to finish the project by the end of 2001,
but now I'm afraid it will have to wait a year,
until after I return from a sabbatical leave.

*Author's note from 2012:
After that sabbatical leave, and one more,
I'm now retired and plan to finally return to this writing project.
But it is still several years from completion,
even if I'm as optimistic as I was 12 years ago.*

Please note that the files listed below are in .pdf format,
suitable for viewing with
Adobe Acrobat Reader.

## Chapter 0: Introduction

** 0.1 **
Some history
(a little about algebra; a little about Göttingen)
** 0.2 **
Vector spaces
(some background for Chapter 2)
** 0.3 **
Abelian groups
(more background for Chapter 2)

## Chapter 1: Rings

** 1.0 **
Richard Dedekind
** 1.1 Basic definitions and examples: **
Problems
| Solutions
** 1.2 Ring homomorphisms: **
Problems
| Solutions
** 1.3 Localization of integral domains: **
Problems
| Solutions
** 1.4 Unique factorization: **
Problems
| Solutions
** 1.5 *Additional noncommutative examples: **

- Review problems
| Solutions

## Chapter 2: Modules

** 2.0 ** Emmy Noether
** 2.1 Basic definitions and examples: **
Problems
| Solutions
** 2.2 Direct sums and products: **
** 2.3 Semisimple modules: **
** 2.4 Chain conditions: **
** 2.5 Modules with finite length: **
** 2.6 Tensor products: **
** 2.7 Modules over principal ideal domains: **

- Review problems
| Solutions

## Chapter 3: Structure of Noncommutative Rings

** 3.0 ** Emil Artin
** 3.1 Prime and primitive ideals: **
** 3.2 The Jacobson radical: **
** 3.3 Semisimple Artinian rings: **

- Review problems
| Solutions

## Appendices, etc.

- Some names
- Biographies (in .html format,
linked to
The MacTutor History of Mathematics archive)
- Timeline
- Bibliography

This page has been accessed
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